neurodudes

A controversial paper proposed that sodium channels are not statistically independent when they open and close. This may have implications for the speed of neural computation.

The following paper proposed that sodium channels are “cooperative”, rather than statistically independent:

Björn Naundorf, Fred Wolf, and Maxim Volgushev. Unique features of action potential initiation in cortical neurons. (there is also a commentary by Boris Gutkin and Bard Ermentrout)

They suggested this because action potentials in real cells exhibit two features that single-compartment Hodgkin-Huxley style models (which assume independence of sodium channels) have trouble accounting for:

• The action potentials begin more abruptly than predicted by the models
• The spike threshold varies over time by as much as 10 mV, whereas the model predicts it should vary by only about 2 mV (they say “onset potential” rather than “threshold” but I’m assuming it’s the same thing?)

The paper shows analytically that in single-compartment Hodgkin-Huxley style models, you can’t get both of these at once (without using unphysiological physical constants). (although in their commentary, Gutkin and Ermentrout say only that “spike speed and onset-voltage variability seem to be antagonistic”; so maybe they think that the original paper’s analytical proof is not airtight?)

They then propose a model in which sodium channels are not statistically independent. Their model predicts that application of the sodium channel blocker TTX should reduce the abruptness of action potential beginnings, whereas Hodgkin-Huxley does not predict this. They do that experiment, and it goes the way they say it should.

It may seem like a small, hard-to-notice difference in the abruptness of action potential onset isn’t important for computation, but in fact the paper argues starting on page 10 of supplementary info part 2 that the sharpness of action potential onset is a limiting factor in how well the neuron can transmit high-frequency signals. Apparently they are arguing that without abrupt spike onsets, the cut-off frequency of the frequency response of the neuron (if you aren’t familiar with frequency response curves, you can pretend that the cut-off frequency is like a CPU clock speed, a maximum frequency of computation, although that’s not quite what it is) is on the order of the mean firing rate. But the cut-off frequency is higher if you have abrupt spike onsets. The result is that you can transmit high-frequency signals without a high mean firing rate if you have very abrupt spike onsets. And this is nice because who wants to have to spike all the damn time? It’s tiring. They also cite two other theory papers in support of this point (1), (2).

But then this paper comes along and tries to refute the original paper:

David A. McCormick, Yousheng Shu and Yuguo Yu. Hodgkin and Huxley model — still standing?

They say that the abrupt spike beginnings and threshold variability can be modeled by Hodgkin-Huxley style models that take spatial geometry into account. Cortical cells have their spike initiation zone in the axon; when the spike is seen in the soma, it has already propagated antidromically from the spike initiation zone to the soma. They claim that the abruptness and threshold variability are a consequence of the propagation, and are not seen at the spike initiation zone; that is, they claim that at the actual spike initiation zone, the spikes do indeed behave as Hodgkin-Huxley style models predict.

They did experiments by cutting the axon of cortical neurons and clamping the cut to show that indeed, at the spike initiation zone the spikes are not so abrupt and do not have so much threshold variability.

Naundorf, Wolf, and Volgushev reply to this refutation by saying that:

• recording from axonal cuts is no good because when you cut the axon you disrupt the entire cytoskelaton, which may disable sodium channel cooperativity if it exists
• the model in the refutation assumes an unphysiologically high ratio of axonal-to-somatic sodium currents
• the model in the refutation does not fit the experimental data. Experimentally, when a spike begins at a relatively low threshold, the membrane voltage begins to increase rapidly while the voltage is still around that low initial voltage. In the model in the refutation, however, the membrane voltage does not increase rapidly until the voltage has increased to a higher level.
• They also cite another paper that provides experimental evidence of abruptness in sodium channel dynamics in nucleated patches, which implies that antidromic propagation cannot be the whole story. What’s a nucleated patch? i think it means pulling off a large patch of the membrane with the electrode, and then letting that patch close off on itself to form a little sphere:
  

The authors posit that because clamping axonal cuts cannot resolve the issue, a better way to resolve it is by looking at the ability of neurons to transmit high-frequency signals. For the same theoretical reasons as before, they argue that Hodgkin-Huxley style models should have cut-off frequencies of about 10 Hz in cells with a mean firing rate of about 10 Hz. And, for the same reasons as before, they argue that their cooperative sodium channel model could have cut-off frequencies of 100 Hz in cells with a mean firing rate of 10 Hz. They then cite two papers as evidence that in fact such cells can transmit 100 Hz signals. I haven’t looked at the first paper yet. The second paper is an experiment in which some neurons phase-locked to a 100 Hz display.

They also have setup a website with further references.

So, who is right? Are sodium channels independent or cooperative? Beats me. Heck, I don’t even know if I’ve correctly understood the arguments so far; lemme know if I got anything wrong. We might not have heard the last of this debate; the third article (the rebuttal to the reply to the original article) was just published Jan 4.

This entry was posted on Monday, January 29th, 2007 at 8:35 pm by Bayle Shanks and is filed under Computational neuroscience, Ion channels. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.